reserve FCPS for up-3-dimensional CollProjectiveSpace;
reserve a,a9,b,b9,c,c9,d,d9,o,p,q,r,s,t,u,x,y,z for Element of FCPS;

theorem Th12:
  ex a,b,c,d st not a,b,c,d are_coplanar
proof
  consider a,b,c,d such that
A1: not a,b,x are_collinear or not c,d,x are_collinear by ANPROJ_2:def 14;
  take a,b,c,d;
  thus thesis by A1;
end;
